what to do with island type faces?
It looks like bad normals and some geometry errors in you model.
Have you tried the classic Select all > Remove Doubles > Recalculate Normals?
(A to select all > W > Remove Doubles then Ctrl + N)

You could then try to use the operator Select Non Manifold Shift + Ctrl + Alt + M to select said faces, although if they are attached to the rest of the model mesh, deleteing then will most likely create more problems for 3D printing, like wholes and discontinuities.

You could then use the Select Non Manifold operator again to detect new problems that might arise and try solve them one by one. Maybe remove doubles and recalculate normals again.